The Theoretical Shapley-Shubik Probability of an Election Inversion in a Toy Symmetric Version of the U.S. Presidential Electoral System

Olivier de Mouzon, Thibault Laurent, Michel Le Breton and Dominique Lepelley
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Olivier de Mouzon: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Thibault Laurent: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Michel Le Breton: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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Abstract: In this article, we evaluate asymptotically the probability ϕ(n) of an election inversion in a toy symmetric version of the US presidential electoral system. The novelty of this paper, in contrast to all the existing theoretical literature, is to assume that votes are drawn from an IAC (Impartial Anonymous Culture)/Shapley–Shubik probability model. Through the use of numerical methods, it is conjectured, that n−−√ϕ(n) converges to 0.1309 when n (the size of the electorate in one district) tends to infinity. It is also demonstrated that ϕ(n)=o(ln(n)3n−−−−√) and ϕ(n)=Ω(1n√).

Keywords: Electoral system; Election Inversions; Impartial Anonymous Culture (search for similar items in EconPapers)
Date: 2020-04
New Economics Papers: this item is included in nep-gth and nep-pol
Note: View the original document on HAL open archive server: https://hal.science/hal-02547744v1
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Published in Social Choice and Welfare, 2020, 54 (2-3), pp.363-395. ⟨10.1007/s00355-018-1162-0⟩

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Related works:
Journal Article: The theoretical Shapley–Shubik probability of an election inversion in a toy symmetric version of the US presidential electoral system (2020)
Working Paper: The Theoretical Shapley-Shubik Probability of an Election Inversion in a Toy Symmetric Version of the U.S. Presidential Electoral System (2018)
Working Paper: The Theoretical Shapley-Shubik Probability of an Election Inversion in a Toy Symmetric Version of the U.S. Presidential Electoral System (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02547744

DOI: 10.1007/s00355-018-1162-0

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